Question

If 2s =a+b+c find (s+a) 3-(s-b)3-3(s+a) (s-b) (a+b)

Answer 1

hola there

I) (s - a)³ + (s - b)³ + 3c(s - a)(s - b) = (s - a)³ + (s - b)³ + 3(s - a)(s - b)(2s - a - b) 
{Since a + b + c = 2s, c = 2s - a - b} 

= (s - a)³ + (s - b)³ + 3(s - a)(s - b){(s - a) + (s - b)} 

ii) Right side of the above is of the form: x³ + y³ + 3xy(x + y) = (x + y)³; 
Here x = s - a and y = s - b 

iii) Hence, right side = (s - a + s - b)³ = (2s - a - b)³ = c³ 

Hence it is proved that: 
(s - a)³ + (s - b)³ + 3c(s - a)(s - b) = c³